a strong city state

Sparta by Alexander's lifetime was anything but. The constant Athenian raids and costly battles of the Peloponnesian War had cost them a huge amount of their precious Spartiate forces and had permanently destroyed the fertility of much of the Peloponnese. Their defeats in the Corinthian War had cost them entire formations of Spartiates wiped out largely by mercenaries and light troops, as well as breaking their nely won hegemony within less than a decade after the end of the Peloponnesian War. And their humiliating defeats at the hands of the Thebans had shattered what little was left of the Spartiate population, and robbed them of arguably their most precious resource, their helots. By Pyrrhus' invasion of Lacedaemon soon after Alexander's death the city of Sparta could field only 300 Spartiates against him, most being old men and boys, and only a couple thousand non-citizens (and the shortage of helots in the city after the liberation of Messenia also severely cut into their numbers). The Spartans did attempt a revolt, fought mostly by their allies, while Alexander was away, but it was the most pathetic of all the Greek revolts during and after Alexander's lifetime. Even with Persian support and a reinforcement of 8000 veteran Greek mercenaries, the survivors of the Issus, Antipater had no trouble absolutely stomping the Spartans out with an army of over 40,000 men, outnumbering the Spartan force by about two-to-one, and outnumbering their actually useful troops by god-knows-how-much. So easily did Antipater think the Spartans would be beaten that he actually delayed in marching on them for some time, dealing with Memnon's attempts to cross over into Thrace instead and allowing the Spartans to build strength through their allies without even worrying about it. Alexander described the rather pathetic battle at Megalopolis as a "battle of mice."

Annihilating the Spartans would've been child's play for Alexander. But why bother? There was nothing in Lacedaemonia, which had suffered severely during the last century's warfare and whose infrastructure was largely non-existent. Lacedaemonia's fairly large iron deposits were worthless to them without their helots, and in any case the Macedonians had iron mines vastly more productive up north. Since their defeat at the hands of the Thebans the Spartans had made no offensive actions, having never left Lacedaemonia, and they really didn't have the ability to do so in the first place--at Megalopolis their forces were almost entirely their allies and mercenaries. Sparta didn't exactly have the greatest diplomatic reputation with any of the states of Greece, being unanimously hated among all of them. Further, the Lacedaemonians were surrounded by strong neighbors, particularly the Messenians (whom the Thebans had artificially strengthened to stomp the Spartans in case they ever tried to re-conquer their former helots) and the strong Macedonian garrison at Corinth. Besides, the Lacedaemonians had accepted Alexander's hegemony, even if they refused to join the League of Corinth. Their inability to provide anything or to undertake any hostile actions without serious outside aid was enough of a reason not to bother delaying the restructuring of Greece and the invasion of Persia (as well as the inevitable casualties even a battle as easy as Megalopolis would've caused--a battle's a battle, after all, and no matter how easy it is somebody on your side is bound to get killed).

It's important to note that Alexander was also spot-on correct in his assessment--the Spartans couldn't do anything without help. Megalopolis was fought pretty much entirely with Persian-provided troops, or troops from cities sympathetic to the Persians, and was funded pretty much entirely with what money the Persians could smuggle across the Aegean, which turned out not to be very much. The Spartan revolt occurred entirely because of Persian diplomatic prodding, not because the Spartans thought of it on their own. This Persian diplomatic meddling is something that happened quite a lot while Alexander was in Asia, and it's an interesting question whether Alexander simply failed to anticipate it, whether he figured his position in Greece was so strong that it didn't matter (which ended up being the case--all the Greek revolts were doomed from the start), or whether the pan-Hellenic rhetoric that Tarn fell for wasn't as successful as he had thought